Treatment failure in neuroblastoma likely involves acquired alkylator resistance and the anti-tumor effect of alkylating agents may be increased by depletion of glutathione (GSH) with the drug buthionine sulfoximine (BSO). This study will evaluate the pharmacokinetics and clinical toxicities of the combination of (BS0) and melphalan in pediatric patients with neuroblastoma. An additional goal of this study is to document GSH depletion in peripheral blood lymphocytes, normal marrow and neuroblastoma cells found in the bone marrow.